Month 
Date 
Topic 
Book 
Notes 


Linear Equations 


January 
5 
Introduction: InitialValue Problems 
14, 15 
1.11.3, 2.1, 2.2 

7 
Homogeneous: Key Identity, Characteristic Polynomials 
17, 22 
2.32.4, 3.13.4 

9 
Nonhomogeneous: Green Functions and Key Identity Evaluations 
18 
4.1, 4.2, 5.4, 5.1 

12 
Nonhomogeneous: Undetermined Coefficients and Composite Forcing 
18 
5.2, 5.3 


Laplace Transform Method 



14 
The Laplace Transform 
48, 49 
6.1, 6.2 

16 
Theory of the Laplace Transform 
49, 51 
6.2 6.3 

21 
Tranform of Derivatives and InitialValue Problems 
50, 51 
6.4, 6.5, 

23 
Piecewice Forcing and Inverse Transforms 
50, 53 
6.6 6.7 

26 
Green Functions, Convolutions, and Impulse Forcing 
52, 53 
6.8, 6.9, 6.10 


Existence and Uniqueness for InitialValue Problems 



28 
Theory for Linear FirstOrder Equations 

7.1, 7.2 

30 
Theory for Separable FirstOrder Eqautions 

7.3 
February 
2 
Theory for General FirstOrder Equations 
68, 69 
7.4 

4 
Finish Picard Theorem Proof, Remarks on Systems 
69, 70 
7.4, 8.18.3 

6 
Midterm Exam 




Fourier Series 



9 
Approximating Periodic Functions 
33 


11 
Fourier Series 
35, 36 


13 
MeanSquare Convergence of Fourier Series 
38 


18 
Scalar Products and Orthogonality 
37 


20 
Pointwise Convergence of Fourier Series 
34, 38 



Application to Partial Differential Equations 



23 
Eigenpairs and the Vibrating String 
39, 40 


25 
OneDimensional Heat Equation 
41 


27 
Laplace Equation over a Disk 
42 

March 
2 
Poisson Integral and SturmLiouville Problems 
42, 43 


4 
SturmLiouville Problems and Orthogonality 
43 



Calculus of Variations 



6 
Introduction, Euler Equations 
65, 66 


9 
Euler Equations, Examples 
66 


11 
Isoparametric Problems 
67 


13 
Isoparametric Problems, Examples 
67 


19 
Final Exam, 11:30am  2:30pm 

